Let μ be a normal function on $[0,1)$ and p>0. Suppose φ is a holomorphic self-map on the unit ball B of ${\mathbf{C}}^{\mathbf{n}}$. In this paper, the authors characterize the conditions such that the composition operator $C_{\phi }$ is bounded or compact from the normal weight Dirichlet type space $D_{\mu }^p(B)$ to the normal weight Bloch type space ${\mathcal{B}}_{{\nu }_p}(B)$ when n>1, where ${\nu }_p(r)=(1-r^2{)}^{\frac{n}{p}}{\mu }^{\frac{1}{p}}(r)$ ($0\le r<1$). Moreover, the authors give a simple sufficient and necessary condition such that $C_{\phi }$ is compact from $D_{\mu }^p(B)$ to ${\mathcal{B}}_{{\nu }_p}(B)$ for some special cases.

中文翻译：

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正常权重狄利克雷型空间与布洛赫型空间的复合算子

令μ是一个正规函数$[0,1)$且p > 0。假设φ是单位球B上的全纯自映射${\mathbf{C}}^{\mathbf{n}}$. 在本文中，作者描述了组合算子的条件$C_{\phi }$从正常权重狄利克雷型空间有界或紧致$D_{\mu }^p(乙)$到正常重量的布洛赫型空间${\mathcal{乙}}_{{\nu }_p}(乙)$当n > 1 时，其中${\nu }_p(r)=(1-r^2{)}^{\frac{n}{p}}{\mu }^{\frac{1}{p}}(r)$($0\le r<1$）。此外，作者给出了一个简单的充分必要条件，使得$C_{\phi }$是紧凑的$D_{\mu }^p(乙)$至${\mathcal{乙}}_{{\nu }_p}(乙)$对于一些特殊情况。